Multiplication and division Multiples, factors and prime numbers Objectives Day 1 Find common multiples and factors. Day 2 Identify prime numbers. Find numbers that have a pair of prime factors. Before teaching, be aware that: On Day 1 children will need mini-whiteboards and pens. You may wish to use the ITP Number Grid. On Day 2 children will need mini-whiteboards and pens. Year 6

Multiplication and division Multiples, factors and prime numbers Starters Day 1 Factors (pre-requisite skills) Day 2 Double and halve numbers to 100 (simmering skills) Choose starters that suit your class by dragging and dropping the relevant slide or slides below to the start of the teaching for each day. Year 6

Multiplication and division Multiples, factors and prime numbers Starter Factors Pre-requisite skills – to use this starter, drag this slide to the start of Day 1 Put children into 4 teams. Each team agree a 2-digit number. Roll a 1–9 dice. If the number rolled is a factor of their number, children put up their hand and the team score a point. Repeat with teams choosing a new 2-digit number. Year 6

Multiplication and division Multiples, factors and prime numbers Starter Double and halve numbers to 100 Simmering skills – to use this starter, drag this slide to the start of Day 2 Children in pairs take it in turns to shuffle a set of 0–9 cards and take 2 to generate a 2-digit number. They choose to double or halve it and mark it on a blank 0–200 line. First to get 5 numbers without their opponent’s numbers in-between wins. Year 6

Multiplication and division Multiples, factors and prime numbers Objectives Day 1 Find common multiples and factors. Year 6

How can we recognise multiples of 9? Day 1: Find common multiples and factors. How can we recognise multiples of 9? Some are also multiples of 6. Write three common multiples of 6 and 9 on your whiteboards. Year 6

What is the lowest common multiple? Day 1: Find common multiples and factors. See how the common multiples have pink and yellow stripes. Check yours. What is the lowest common multiple? Year 6

Day 1: Find common multiples and factors. Which of these multiples of 6 are also multiples of 8? What is the smallest common multiple? Year 6

Now look for common factors and ring them. Day 1: Find common multiples and factors. Work in pairs to list all the factors of each number: one person lists the factors of 18, the other lists the factors of 24. Now look for common factors and ring them. What is the highest common factor? (The biggest number that goes into both 18 and 24. Now work in pairs to list all the factors of 24 and 32. Then ring common factors and find the highest common factor. Agree the common factors of 18 and 24 as 1, 2, 3, 6, and 6 as the highest common factor, the biggest number that will ‘go into’ both. Children can now go on to do differentiated GROUP ACTIVITIES. You can find Hamilton’s group activities in this unit’s TEACHING AND GROUP ACTIVITIES download. WT: Game to find a number on the grid that is a common multiple of numbers on 2 cards. Then identify factors of numbers on a grid. ARE/GD: Two games: Shuffle cards, take 2 and say a common multiple. Choose a number from a grid and say a factor. Child with highest factor wins. Year 6

The Practice Sheet on this slide is suitable for most children. Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. GD: Children also complete the challenges. Challenge Challenge Year 6

Multiplication and division Multiples, factors and prime numbers Objectives Day 2 Identify prime numbers. Find numbers that have a pair of prime factors. Year 6

Day 2: Identify prime numbers; Find numbers that have a pair of prime factors. Numbers with only two factors: themselves and 1, are called prime numbers. 2 is the smallest prime, as 1 just has 1 factor not 2. Numbers that have more than themselves and 1 as factors are called composite numbers. 2 3 5 7 11 13 17 19 Work in pairs to list all the numbers from 2 to 10 which are primes. Now work in pairs to list all the numbers from 10 to 20 which are primes. Today would be a great day to use a problem-solving investigation – Magic Multiplication Squares – as the group activity, which you can find in this unit’s IN-DEPTH INVESTIGATION box on Hamilton’s website. Alternatively, children can now go on to do differentiated GROUP ACTIVITIES. You can find Hamilton’s group activities in this unit’s TEACHING AND GROUP ACTIVITIES download. WT/ARE: Find which numbers from 10 to 30 can be made by multiplying 2 prime numbers together. GD: Write numbers as product of several prime factors. Now think of a number between 10 and 20 which has the following factors: 1, itself, two prime numbers. 15 Year 6

The Practice Sheet on this slide is suitable for most children. Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. WT: List prime numbers from 20 to 30. Find numbers which can be made by multiplying 2 prime numbers together. ARE/GD: List prime numbers from 20 to 40. Find numbers which can be made by multiplying 2 prime numbers together. Challenge Year 6

Multiplication and division Multiples, factors and prime numbers Well Done! You’ve completed this unit. Objectives Day 1 Find common multiples and factors. Day 2 Identify prime numbers. Find numbers that have a pair of prime factors. You can now use the Mastery: Reasoning and Problem-Solving questions to assess children’s success across this unit. Go to the next slide. Year 6

Multiplication and Division Problem solving and reasoning questions    Which pair of numbers under 20 have the largest number of common factors? What is the highest common factor? Write common multiples of 4 and 6 up to 60. What is the lowest common multiple? Use this information to find the lowest common multiple of 8 and 12. True or false • The lowest common multiple of two prime numbers, a and b is always a x b. • The highest common factor of two multiples of 6 is always 6. Year 6

Problem solving and reasoning answers    Which pair of numbers under 20 have the largest number of common factors? What is the highest common factor? 6 and 12 and 8 and 16 each have four common factors: 6 and 12 have common factors of 1, 2, 3 and 6 (highest). 8 and 16 have common factors of 1, 2, 4 and 8 (highest). Write common multiples of 4 and 6 up to 60. What is the lowest common multiple? Use this information to find the lowest common multiple of 8 and 12. 12 (lowest), 24, 36, 48 and 60. True or false • The lowest common multiple of two prime numbers, a and b is always a x b. True, since they are prime numbers they will have no other factors so cannot have any other multiples in common. • The highest common factor of two multiples of 6 is always 6. False, as long as one of the numbers is a multiple of the other there will be a higher common factor, e.g. 12 and 24. Year 6